Determine the Nash Equilibrium by Backward Induction. Stop -1,-1,8 Go 5,-15, 10 Stop 5, 10,-7 Go 10,-9,6 Stop -5,8,-7 Go -2,5,0 Stop 5,-8, 20 Go 10,-12,0 A UP DOWN O (5, 10,-7) O (5,-8, 20) O (10,-9,6) O (10,9,6) B B LEFT RIGHT LEFT C C C RIGHT C
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- Purchase of a product The market research department at a manufacturing plant determines that 20 of the people who purchase the plants product during any month will not purchase it the next month. On the other hand, 30 of the people who do not purchase the product during any month will purchase it in the next month. In a population of 1000 people, 100 people purchased the product this month. How many will purchase the product a next month and b in 2 months?Customer Preference Two movie theatres that show several different movies each night compete for the same audience. Of the people who attend theatre A one night, 10 will attend again the next night and 5 will attend Theatre B the next night. Of the people who attend Theatre B one night, 8 will attend again the next night and 6 will attend Theatre A the next night. Of the people who attend neither theatre one night, 3 will attend Theatre A the next night and 4 will attend Theatre B the next night. Find and interpret the steady state matrix for this situation.Lottery Powerball is a lottery game that is operated by the Multi-State Lottery Association and is played in 44 states, Washington D.C., Puerto Rico, and the U.S. Virgin Islands. The game is played by drawing five white balls out of a drum of 69 white balls (numbered 1-69) and one red powerball out of a drum of 26 red balls (numbered 1-26). The jackpot is won by matching all five white balls in any order and the red powerball. (a) Find the possible number of winning Powerball numbers. (b) Find the possible number of winning Powerball numbers when you win the jackpot by matching all five white balls in order and the red powerball.
- N5 Suppose that you have a group of 10 people (where any two people are either friends or enemies) and one person has at least 6 enemies. Prove that there are either three mutual friends or four mutual enemies.In Hotelling's Ice Cream Truck game. Assume there are 9 spots: {-4, −3, −2, −1, 0, 1, 2, 3, 4}Assume there are two customers at each spot (18 in total). In a Nash equilibrium, each truck will locate at 0. How many customers would truck A lose by deviating and moving from position 0 to position 1. Select one: a.none of the other answers. b.3 c.1 d.0 e.2The following table shows the performance of a selection of 100 fictitious stocks after one year. (Take S to be the set of all stocks represented in the table.) Companies Pharmaceutical Electronic Internet (P) (E) (1) Total Increased (V) 5 15 25 Unchangedt (N) 30 20 50 Decreased (D) 5 5 15 25 Total 40 10 50 100 Calculate (V n) n(I) stocks What does the answer represent? n(Vn1) is the fraction of Internet stocks that increased in value. n(1) n(Vn1) is the fraction of Internet stocks that remained unchanged in value. n(1) n(Vn1) n(1) is the fraction of Pharmaceutical stocks that increased in value. n(Vn1) is the fraction of Electronic stocks that increased in value. n(1) n(Vn1) n(1) is the fraction of Internet stocks that decreased in value.
- Q.1) What are the possible number of Boolean functions with n-ternary variable?a) Two events, A and B, are such that P(A∪B) = 0.86, P(B) = 0.72 and P(A) = 0.64. Determine (i) P (A∩B ) [2] (ii) P(A/B) [2] (iii) P(AUB)' [1]A game is called zero-sum if Vi, j : R(di, &j) + S(di, &j) = c O a. True O b. False A move d' is dominated is Vd & D with d ‡ d', vô A, R(d', ) ≤ R(d, 6) O a. False O b. True MAGNUMMECECE If a game is separable, then m = n. O a. False O b. True The following matrix 17 0 0 -17 defines a separable zero-sum game. O a. False O b. True
- A roulette wheel has 30 slots, consisting of 2 blues, 8 whites, and 20 red slots. You will receive P100 if the roulette stops spinning on a blue slot, you will receive P50 on a white slot, but you will be penalized P10 if the roulette stops spinning on a red slot. Let X be the amount you will recieve (or pay). The probaility of receiving P50 is 2/30 or 1/15, and of receiving P50 is 8/30 or 4/15. What is the probability of penalty of P10? 2/3 1/3 -2/3A mouse is trapped in maze (a room having labyrinths) with three exits at the center of maze. Exit-1 leads outside the maze after 3 minutes. Exit-2 leads backs to the room after 5 minutes. Exit-3 leads backs to the room after 7 minutes.Every time the mouse makes a choice, it is equally likely to choose any of the three exits. What is the expected time taken for the mouse to leave the maze?The following table shows the performance of a selection of 100 fictitious stocks after one year. (Take S to be the set of all stocks represented in the table.) Companies Pharmaceutical Electronic Internet (E) (P) (I) Total Increased (V) 10 5 15 30 Unchangedt (N) 35 40 Decreased (D) 10 5 15 30 Total 55 10 35 100 n(V n I) Calculate n(I) stocks What does the answer represent? n(V n I) is the fraction of Electronic stocks that increased in value. n(1) n(V n I) is the fraction of Internet stocks that remained unchanged in value. n(I) n(V n I) is the fraction of Internet stocks that decreased in value. n(I) n(V n I) is the fraction of Pharmaceutical stocks that increased in value. n(I) n(V n I) is the fraction of Internet stocks that increased in value. n(I)